#### Assertion: In a hexagonal close-packed (HCP) structure, the ratio of the height of the unit cell to the length of the sides of the base is$\sqrt{3}:2.$Reasoning: The HCP structure can be considered as a stacking of close-packed layers of spheres, where the spheres in the second layer lie in the depressions of the first layer.Option: 1 Both Assertion and Reasoning are true, and Reasoning is the correct explanation of Assertion.  Option: 2 Both Assertion and Reasoning are true, but Reasoning is not the correct explanation of Assertion.Option: 3 Assertion is true, but Reasoning is false.Option: 4 Assertion is false, but Reasoning is true.

The hexagonal close-packed (HCP) structure is a type of close-packed structure in which the atoms are arranged in a hexagonal pattern with an ABABAB stacking sequence. In this structure, each atom is in contact with 12 other atoms, resulting in a coordination number of 12.The unit cell of an HCP structure is a hexagonal prism with a top and bottom hexagonal face and 6 rectangular faces. The height of the unit cell is the distance between the top and bottom hexagonal faces, and the length of the sides of the base is the distance between two opposite corners of the hexagon.The ratio of the height of the unit cell to the length of the sides of the base in an HCP structure is $\sqrt{3}:2.$This can be derived by considering the arrangement of atoms in the structure. In an HCP structure, the spheres in the second layer lie in the depressions of the first layer, resulting in a stacking sequence of ABABAB. This arrangement of atoms results in a hexagonal prism with a height that is $\sqrt{3}$ times the distance between two adjacent spheres in the same layer and a base that is twice the distance between adjacent spheres along the same layer. Thus, the ratio of the height to the length of the sides of the base is  $\sqrt{3}:2.$In summary, the Assertion-Reasoning statement is true, and Reasoning provides a correct explanation of Assertion. The ratio of the height of the unit cell to the length of the sides of the base in an HCP structure is indeed$\sqrt{3}:2,$which can be derived by considering the arrangement of atoms in the structure.

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